Results 11 to 20 of about 285 (163)
Abelian ideals of Borel subalgebras and affine Weyl groups
Advances in Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
PAPI, Paolo, Paola Cellini
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Very nilpotent basis and n-tuples in Borel subalgebras [PDF]
Comptes Rendus. Mathématique, 2010 A (vector space) basis B of a Lie algebra is said to be very nilpotent if all the iterated brackets of elements of B are nilpotent. In this Note, we prove a refinement of Engel's Theorem. We show that a Lie algebra has a very nilpotent basis if and only
Michaël Bulois +2 more
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Uniqueness up to inner automorphism of regular exact Borel subalgebras
Advances in MathematicsKülshammer, König and Ovsienko proved that for any quasi-hereditary algebra $(A,\leq_A)$ there exists a Morita equivalent quasi-hereditary algebra $(R, \leq_R)$ containing a basic exact Borel subalgebra $B$. The obtained Borel subalgebra is in fact a regular exact Borel subalgebra.
Rasmussen, Anna Rodriguez
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Young diagrams, Borel subalgebras and Cayley graphs
Let $\mathtt{k}$ be an algebraically closed field of characteristic zero and $n, m$ coprime positive integers. Let ${\stackrel{\rm o}{\mathfrak{g}}}$ be the Lie superalgebra ${\mathfrak{sl}}(n|m)$ and let $\mathfrak T_{iso}$ be the groupoid introduced by Sergeev and Veselov \cite{SV2} with base the set of odd roots of ${\stackrel{\rm o}{\mathfrak{g}}}$
Musson, Ian M.
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From quasi‐hereditary algebras with exact Borel subalgebras to directed bocses [PDF]
, 2020 Up to Morita equivalence, every quasi-hereditary algebra is the dual algebra of a directed bocs or coring. From the bocs, an exact Borel subalgebra is obtained.
Tomasz Brzezinski +3 more
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Elementary Lie Algebras and Lie A-Algebras. [PDF]
, 2007 A finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. The present paper is primarily concerned with the classification of
Varea, Vicente R., Towers, David A.
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Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz.Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the quantum affine ...
Samuel Belliard +3 more
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Presentation by Borel subalgebras and Chevalley generators for quantum enveloping algebras [PDF]
, 2006 We provide an alternative approach to the Faddeev–Reshetikhin–Takhtajan presentation of the quantum group U_q(g), with L-operators as generators and relations ruled by an R-matrix. We look at U_q(g) as being generated by the quantum Borel subalgebras U_q(
GAVARINI, Fabio
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Equivalence Classes of Ideals in the Nilradical of a Borel Subalgebra [PDF]
Nagoya Mathematical Journal, 2006 AbstractAn equivalence relation is defined and studied on the set of B-stable ideals in the nilradical of the Lie algebra of a Borel subgroup B. Techniques are developed to compute the equivalence relation and these are carried out in the exceptional groups.
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Nilpotent subalgebras of semisimple Lie algebras [PDF]
, 2009 Let g be the Lie algebra of a semisimple linear algebraic group. Under mild conditions on the characteristic of the underlying field, one can show that any subalgebra of g consisting of nilpotent elements is contained in some Borel subalgebra.
Levy, Paul +6 more
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